Tc Calculator

Estimate the Time of Concentration ($T_c$) for a catchment using six well-established methods. This guide explains what each formula represents, when to use it, the parameter ranges to watch for, and how to interpret comparison results across methods.

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Overview

The Time of Concentration ($T_c$) is the time required for runoff to travel from the hydraulically most distant point in a catchment to the outlet. It is one of the most influential inputs in peak-discharge calculations, directly driving the design rainfall intensity read from an IDF curve and therefore feeding into the Rational Method, the SCS TR-55 family of procedures, the SANRAL SCS method, and SDF / Unit Hydrograph approaches.

$T_c$ depends primarily on three catchment characteristics: flow-path length, slope, and surface roughness. A longer, flatter, or rougher flow path produces a longer $T_c$, which in turn produces a lower design intensity and a lower peak flow for a given return period. Because the design intensity moves with $T_c$, the method is sensitive — a 20% shift in $T_c$ can translate directly into a 10 – 20% shift in the estimated peak discharge.

Why Tc matters

$T_c$ determines the critical storm duration used in design flood calculations. An underestimated $T_c$ produces an over-conservative design (unnecessarily large and costly infrastructure); an overestimated $T_c$ produces an unsafe design. Selecting the appropriate method — and verifying that the catchment falls within its range of applicability — is fundamental to defensible hydrological engineering.

What is Tc?

Conceptually, $T_c$ is the sum of the travel times along the longest hydraulic flow path from the catchment divide to the outlet. Most empirical formulas lump these travel times into a single correlation with length, slope, and a roughness or land-cover parameter. The more detailed methods (notably the FHWA 3-component approach) break the flow path into physically distinct segments and compute a travel time for each.

Two conventions to keep in mind when working with $T_c$:

• Units matter. Kirpich, NRCS lag, FAA, and Kerby in their classical forms use imperial units (feet, ft/ft, %). The SA SCS (SANRAL) method uses metric units natively. The calculator handles unit conversions internally — the formulas shown below are given in the units most commonly cited in the original literature.
• $T_c$ vs lag time ($T_L$). Several methods (notably NRCS) are formulated in terms of the watershed lag $T_L$, where $T_c \approx T_L / 0.6$. The calculator returns $T_c$ in minutes in all cases; the conversion is applied automatically for lag-based formulas.

Getting started

Using the calculator follows a simple four-step workflow:

1. Open the calculator from the Tools menu or at /tc-calculator/new.
2. Select a method (Kirpich, NRCS, FAA, Kerby, SA SCS, or FHWA 3-component), or switch to Comparison Mode to run all applicable methods at once.
3. Enter the required inputs — flow-path length, slope, and the method-specific parameter (k-factor, Curve Number, runoff coefficient, retardance, or segmented flow data).
4. Calculate — the tool returns $T_c$ in minutes, flags any parameters that fall outside the method’s recommended range, and lets you save the result for use in downstream tools.

Quick start

If you are unsure which method fits your catchment, start in Comparison Mode. Running all methods simultaneously immediately surfaces whether the estimates cluster tightly (a good sign that your inputs are self-consistent) or spread widely (a signal to investigate which methods are being applied outside their intended range).

Calculation methods

The calculator supports six widely-used methods. All methods return $T_c$ in minutes.

Kirpich (1940)

One of the earliest and most widely used empirical formulas. Developed by Z.P. Kirpich from rainfall-runoff data on seven small agricultural watersheds in Tennessee, ranging from 0.4 to 45 hectares. It remains a workhorse for small rural catchments and appears as the default Tc method in many regional drainage guidelines.

$$T_c \;=\; 0.0078 \cdot k \cdot \left(\frac{L}{\sqrt{S}}\right)^{0.77}$$

Kirpich equation (imperial units)

Where $L$ = watercourse length (ft), $S$ = average slope (ft/ft), and $k$ = surface-type adjustment factor. The result is in minutes.

The original Kirpich coefficient was calibrated for bare-soil channels. The $k$ adjustment lets you correct for surface roughness outside that calibration — reducing $T_c$ for smooth paved channels and increasing it for vegetated or forested ones.

Surface type	k-value
Concrete / asphalt	0.2
Bare soil	0.4
Poor grass / cultivated	0.6
Average grass	1.0
Dense grass / woodland	2.0

Best for

Small rural or agricultural catchments (≲ 50 ha) with well-defined channelised flow and slopes in the range 3 – 10%. Outside this range — very flat catchments, heavily urbanised areas, or catchments dominated by sheet flow — Kirpich systematically under-predicts $T_c$ and should be cross-checked against at least one other method.

NRCS / SCS lag

Developed by the US Natural Resources Conservation Service (formerly the Soil Conservation Service) and documented in the NRCS National Engineering Handbook, Chapter 15. The method estimates the watershed lag $T_L$ from hydraulic length, slope, and the SCS Curve Number — which captures the combined effect of land cover, soil hydrologic group, and antecedent moisture — and converts to $T_c$ via $T_c = T_L / 0.6$.

$$T_L \;=\; \frac{L^{0.8} \cdot \left(\dfrac{1000}{CN} - 9\right)^{0.7}}{1900 \cdot \sqrt{Y}}$$

NRCS lag equation (imperial units, result in hours)

Where $L$ = hydraulic length (ft), $CN$ = SCS Curve Number (30 – 98), and $Y$ = average watershed slope (%). The calculator returns $T_c$ in minutes after conversion from $T_L$.

Curve Number selection

$CN$ values above about 90 represent nearly impervious or already-saturated surfaces; values between 70 and 85 are typical of medium-density urban areas and cultivated land; values of 50 – 65 represent well-drained, vegetated catchments with significant infiltration. NRCS NEH-4, Chapter 9 tabulates CN by hydrologic soil group (A–D) and land cover, and that table should be the reference for any NRCS-based calculation.

Limits of applicability

The NRCS lag method was calibrated for catchments smaller than about 8 km² with slopes between 0.5% and 30%. It tends to over-predict $T_c$ for urban catchments with significant channelised flow, which is why the NRCS recommends the 3-component segmented method (also implemented here) for urban work.

FAA rational

Developed by the US Federal Aviation Administration for airport drainage design and published in FAA Advisory Circular 150/5320-5. The formula is intended for overland flow on smooth, well-defined surfaces — airport pavements, parking lots, and small planned drainage areas — where the Rational Method runoff coefficient $C$ is already known.

$$T_c \;=\; \frac{1.8 \cdot (1.1 - C) \cdot \sqrt{L}}{(100 \cdot S)^{1/3}}$$

FAA rational equation (imperial units)

Where $C$ = Rational Method runoff coefficient (0.0 – 1.0), $L$ = flow-path length (ft), and $S$ = surface slope (%). Result is in minutes.

Because the formula shares the runoff coefficient $C$ with the Rational Method, it is convenient as a self-consistent pairing: the same value of $C$ used in the peak-flow calculation feeds into $T_c$, which sets the rainfall intensity used in the same peak-flow calculation.

Best for

Small, highly-developed drainage areas — airport pavements, car parks, and small commercial or residential developments — where overland flow dominates and $C$ can be estimated with confidence. Avoid using this method for rural or mixed-cover catchments; it was not calibrated for them.

Kerby (1959)

Specifically formulated for overland (sheet) flow conditions, where water moves as a thin film across the surface without concentrating into channels. The Kerby method is often used to estimate the initial sheet-flow component of $T_c$ in segmented calculations.

$$T_c \;=\; 0.8268 \cdot \left(\frac{L \cdot r}{\sqrt{S}}\right)^{0.467}$$

Kerby equation (imperial units)

Where $L$ = overland flow length (ft, limited to 1,200 ft / 365 m), $r$ = retardance coefficient, and $S$ = surface slope (ft/ft). Result is in minutes.

The retardance coefficient $r$ encodes the combined effect of vegetation, surface roughness, and litter depth on sheet-flow velocity:

Surface type	Retardance (r)
Smooth impervious (asphalt, concrete)	0.02
Smooth bare packed soil	0.10
Poor grass, cultivated row crops	0.20
Deciduous forest	0.40
Dense grass, coniferous forest	0.60
Dense grass with deep mulch	0.80

Flow-length limit

Kerby is only valid for overland flow paths up to 365 m (1,200 ft). Beyond that length, flow almost always concentrates into rills or channels, and continuing to apply Kerby will over-predict travel time. For longer flow paths, use Kirpich, NRCS, or the FHWA 3-component method, or split the path and use Kerby only for the sheet-flow segment.

SA SCS (SANRAL)

The South African adaptation of the SCS method, as prescribed in the SANRAL Drainage Manual. This is the default $T_c$ method used in South African drainage practice for watercourse routing, SCS peak-flow estimation, and the Unit Hydrograph method. It is formulated in metric units natively and produces results that are consistent with the SANRAL SCS and Unit Hydrograph procedures.

$$T_c \;=\; \left(\frac{0.87 \cdot L^2}{1000 \cdot S_{avg}}\right)^{0.385}$$

SA SCS equation (metric units, result in hours)

Where $L$ = hydraulic length of the watercourse (km), $S_{avg}$ = average slope along the main watercourse (m/m). The calculator converts the result to minutes.

South African projects

For any project in South Africa, the SA SCS (SANRAL) method should be the starting point. It is the method tested against local rainfall-runoff records and is the one referenced by the design standards that regulators and peer reviewers will apply to your work. Use Kirpich or NRCS as cross-checks, not substitutes.

FHWA 3-component

The most physically-based method available. Developed by the Federal Highway Administration and documented in FHWA HDS-2 (Highway Hydrology, 2nd edition). It segments the flow path into three distinct flow regimes, computes a travel time for each, and sums them:

Component	Method	Description
Sheet flow	Manning kinematic wave	Thin sheet flow on the upper catchment. Limited to about 90 m (300 ft). Uses Manning’s $n$ and the 2-year, 24-hour rainfall depth.
Shallow concentrated flow	Velocity-based (HDS-2 Fig. 2.2)	Flow concentrates in rills, swales, or gutters. Velocity is estimated from slope and surface type (paved or unpaved).
Channel flow	Manning’s equation	Open-channel flow in a defined watercourse. Requires channel geometry (area, wetted perimeter), slope, and Manning’s $n$ for the channel.

$$T_c \;=\; T_{\text{sheet}} + T_{\text{shallow}} + T_{\text{channel}}$$

FHWA 3-component total

The sheet-flow component uses the kinematic wave solution:

$$T_{\text{sheet}} \;=\; \frac{0.007 \cdot (n \cdot L)^{0.8}}{P_2^{0.5} \cdot S^{0.4}}$$

Sheet flow (Manning kinematic wave, imperial)

Where $n$ = Manning’s roughness for sheet flow, $L$ = sheet-flow length (ft, ≤ 300 ft), $P_2$ = 2-year 24-hour rainfall depth (in), and $S$ = slope (ft/ft). Result in hours.

When to use FHWA

The FHWA 3-component method is the right choice when you have good information about the flow path — distinct surface types, a defined channel at the lower end, and plausible values for Manning’s $n$, channel cross-section, and slope at each segment. It is the most defensible method for complex urban or mixed-cover catchments and is the one the NRCS now recommends over the single-equation NRCS lag for urban work.

Comparison mode

Comparison mode runs every applicable method against the same inputs and displays the results side-by-side. It is especially useful early in a design, when you are still deciding which method best fits the catchment, and as a sensitivity check before locking in a peak-flow estimate.

• Side-by-side results. All method outputs appear in a single table with $T_c$ in minutes.
• Applicability flags. Methods applied outside their recommended parameter ranges (e.g. Kerby with $L > 365$ m, Kirpich with very flat slopes) are flagged with a warning so they can be excluded from the decision.
• Sensitivity at a glance. When multiple methods agree to within ~20%, the estimate is likely robust. When they disagree by a factor of two or more, at least one method is being applied outside its intended range.

Engineering judgement

Large discrepancies between methods are a diagnostic, not a problem. Check the applicability ranges (slope, length, imperviousness), verify the input data, and pick the method that best matches the dominant flow regime of the catchment. Document the choice in the design report — a Tc selection rationale carries weight with reviewers.

Method selection

Selecting a method depends on catchment size, flow regime, land use, available data, and project location. The table below is a starting point — it is not a substitute for engineering judgement.

Scenario	Recommended method
Small rural / agricultural catchment (< 50 ha)	Kirpich or NRCS/SCS lag
Small urban drainage area with known $C$	FAA rational
Pure overland / sheet flow, $L$ < 365 m	Kerby
South African catchment, any size	SA SCS (SANRAL) — cross-check with Kirpich / NRCS
Complex urban or mixed-cover catchment	FHWA 3-component
Preliminary estimate, uncertain catchment character	Comparison mode (all methods)

No single best method

There is no universally correct $T_c$ method. Each was calibrated for specific conditions and carries its own assumptions. The professional standard is to compute $T_c$ by at least two methods wherever the data allow, document the choice, and sanity-check the result against the expected physical behaviour of the catchment.

Choosing between methods

A quick decision guide for common cases:

• Kirpich — Good default for natural, channelised watersheds up to ~50 ha.
• NRCS / SCS lag — When you have a reliable Curve Number and a non-urban catchment smaller than about 8 km².
• FAA rational — Small, predominantly impervious catchments where $C$ is already known for the Rational Method.
• Kerby — Sheet-flow component only (pair with another method for the channelised part of the path).
• SA SCS (SANRAL) — Default for South African projects; results are consistent with the SANRAL Drainage Manual procedures.
• FHWA 3-component — Most physically rigorous; use when flow segments are clearly identifiable and Manning’s $n$ values are defensible.

Limitations

Every $T_c$ method carries inherent limitations that engineers should be explicit about in design reports:

• Applicability ranges. Each formula was calibrated for a specific range of catchment size, slope, and land cover. Applying a method outside its range produces unreliable results. The calculator flags common breaches (e.g. Kerby beyond 365 m), but the responsibility for staying within the calibration envelope rests with the user.
• Uniform-conditions assumption. Most single-equation methods assume uniform slope, surface roughness, and rainfall distribution across the catchment. Real catchments rarely meet this ideal, which is one of the reasons to cross-check with a second method or a segmented approach.
• Empirical by construction. Kirpich, NRCS lag, Kerby, and FAA are all empirical relationships derived from observed data in specific geographies. Transferring them to markedly different climatic or physiographic settings (e.g. Kirpich in very flat Highveld terrain) introduces unquantified bias.
• Steady-state assumption. All methods assume the full catchment is contributing at $T_c$. For very large catchments, partial-area effects can dominate the design peak and a deterministic hydrograph method (Unit Hydrograph, SDF, or a hydrological model) is required.
• Field verification. Wherever historical flood records or gauged data exist, computed $T_c$ should be sanity-checked against the observed lag between storm centroid and peak discharge. Significant disagreement is a signal to revisit the inputs or the method choice.

Professional judgement required

$T_c$ estimation is not a purely mechanical exercise. Results should be reviewed by a qualified engineer with knowledge of the local catchment, and any significant departures from expected values should trigger investigation before they flow through into a peak-flow or design value.

References

• Kirpich, Z.P. (1940). Time of concentration of small agricultural watersheds. Civil Engineering, 10(6), 362.
• NRCS. (2010). National Engineering Handbook, Part 630 — Hydrology, Chapter 15: Time of Concentration. United States Department of Agriculture, Natural Resources Conservation Service.
• NRCS. (1986). Urban Hydrology for Small Watersheds (TR-55). United States Department of Agriculture, Natural Resources Conservation Service.
• Federal Aviation Administration. (2016). Advisory Circular 150/5320-5B: Airport Drainage Design. US Department of Transportation.
• Kerby, W.S. (1959). Time of concentration for overland flow. Civil Engineering, 29(3), 174.
• SANRAL. (2013). Drainage Manual (6th ed.). South African National Roads Agency, Pretoria. Chapter 3 — Hydrology.
• FHWA. (2002). Highway Hydrology (HDS-2, 2nd ed.). Federal Highway Administration, US Department of Transportation.
• FHWA. (2009). Urban Drainage Design Manual (HEC-22, 3rd ed.). Federal Highway Administration, US Department of Transportation.
• ASCE. (1992). Design and Construction of Urban Stormwater Management Systems. ASCE Manuals and Reports of Engineering Practice No. 77.

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